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A typical 1000-MW electrical generating power plant produces 1 .0 × 10 3 megajoules (MJ) in 1 s. How many kilocalories does it produce in 1 s? If its efficiency is 34%, how much energy (in MJ) does it consume in 1 s? If the power plant were coal fired, how many kilograms of coal would it consume in 1 s? If the power plant were natural gas fired, how many kilograms of natural gas would it consume in 1 s?

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Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692

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Chapter
Section
BuyFindarrow_forward

Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692
Chapter 9, Problem 44E
Textbook Problem
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A typical 1000-MW electrical generating power plant produces 1 .0 × 10 3 megajoules (MJ) in 1 s.

How many kilocalories does it produce in 1 s?

If its efficiency is 34%, how much energy (in MJ) does it consume in 1 s?

If the power plant were coal fired, how many kilograms of coal would it consume in 1 s?

If the power plant were natural gas fired, how many kilograms of natural gas would it consume in 1 s?

Interpretation Introduction

Interpretation:

The energy produced (in kilocalories) in 1 second and the consumption of coal and natural gas (in kilogram) are to be calculated.

Concept introduction:

The power derived from the utilization of chemical or physical resources to provide heat and light or to carry out various processes is known as energy. The SI unit of energy is joule.

Unit conversion is a multiple-step process that is used to convert the unit of measurement of a given quantity. It is determined by multiplicaiton with a conversion factor.

The useful energy derived can be calculated by using the equation:

Total consumed×efficency=useful energy.

Conversion factor megajoules to joule is 106 J1 MJ

Conversion factor calorie to kilocalorie is 1 kcal1000 cal

Explanation of Solution

a) The number of kilocalories produce in 1 s.

The energy produced in one second by the power plant is given as:

Energy=1.0 ×103megajoules/second

The kilocalorie produced in one second is calculated as follows:

First, convert megajoule into joule, then joule into calorie, and then calorie into kilocalorie.

Conversion of megajoule into kilocalorie is as follows:

4.18 joule=1 calorie `

E=(1000 MJsec)×(106 J1 MJ)×(1 cal4.18 J)×(1 kcal1000 cal)=2.4×105 kcal/sec

Therefore, the kilocalorie produced in one second is 2.4×105 kcal/sec.

b) The amount of energy it consumes in 1 s if its efficiency is 34%.

The total energy consumed in one second is calculated as follows:

The equation used to calculate the total energy consumed is represented as follows:

Total consumed×efficency=useful energy

The total energy produced in one second is 2.4×105 kcal/sec. (From subpart a)

The efficiency of a person is 34%.

Conversion of percentage into decimal:

Efficiency=34%Efficiency=34100Efficiency=0.34

Substitute the values in the given equation:

2.4×105 kcal/sec=total consumed×0.34(2.4×105 kcal/sec0.34)=total consumed7.1×105 kcal/sec=total consumed

Or

The energy consumed in MJ is calculated as follows:

1000 MJ=total consumed×0.34(1000 MJ0

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